A hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. an association gives a dinner and charges $3 a plate but invites for non paying guests. if each person has one plate, how many paying persons must attend for the association to collect the exact amount to pay the hotel?

40

Step-by-step explanation:

20 + 2.5x = 3x

20 = 0.5x

x = 40

64 paying persons must attend for the association to collect the exact amount to pay the hotel.

Step-by-step explanation:

Let x represent the number of paying guests that would attend the occasion.

The hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. This means that the total charge for x paying guests would be

2.5x + 20

The association gives a dinner and charges $3 a plate but invites four non paying guests. If each one has a plate and 4 guests are not paying, then the revenue that can be generated would be

3(x - 4)

For the association to collect the exact amount to pay the hotel, the number of paying persons that must attend would be

2.5x + 20 = 3(x - 4)

2.5x + 20 = 3x - 12

3x - 2.5 = 20 + 12

0.5x = 32

x = 32/0.5

x = 64

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.